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### Dished Head Equation and Calculator Pressure Vessel Equations and Calculator

ASME Pressure Vessel Design and Engineering

ASME Pressure Vessel Section I: Dished Heads Formulae: Equations and Calculator:

Dished heads can be manufactured using a combination of processes, spinning & flanging, where the spherical radius is made via the spinning process and the knuckle is created under the flanging method. Flanged and dished heads can be formed in a size range from 4 in to 300 in diameter and in thickness range of 14 Gauge to 1-1/2” thick. Pressure vessel heads and dished ends are essentially the same the end caps of a pressure vessel tank or an industrial boiler, supplied with a flanged edge to make it easier for the fabricator to weld the head to the main body of the tank.

Paragraph PG-29.1 states that the thickness of a blank, unstayed dished head with the pressure on the concave side, when it is a segment of a sphere, shall be calculated by the following formula:

Where:
t = Minimum thickness of head (in);
P = maximum allowable working pressure (psi);
L = Concave side radius (in);
S = Maximum Allowable Working Stress (psi). According to ASME Section II, Table 1A.

Paragraph PG-29.2 states: “The radius to which the head is dished shall be not greater than the outside diameter of the flanged portion of the head. Where two radii are used, the longer shall be taken as the value of L in the formula.”

Example:

Segment of a Spherical Dished Head:
Calculate the thickness of a seamless, blank unstayed dished head having pressure on the concave side. The head has an inside diameter of 42.7 in. with a dish radius of 36.0 in. The Maximum Allowable Working Pressure (MAWP) is 360 psi and the material is SA-285 A. The temperature does not exceed 480°F. State if this thickness meets Code.

P = 360 psi;
L = 36.0 in;
S = 11,300 psi – SA-285 A at 480°F.

t = [5 ( 360 x 36 ) ]/ [ 4.8 ( 11,300 ) ]
t = 1.195 in.